Interacting Anyonic Fermions in a Two-Body Color Code Model

TL;DR

This paper presents a two-body spin-1/2 lattice model with topological degeneracy, hosting interacting anyonic fermions and a gapped phase resembling a color code, with implications for topological quantum computation.

Contribution

It introduces a novel two-body Hamiltonian model with exact topological degeneracy and interacting anyonic fermions, expanding the understanding of topological phases.

Findings

Model exhibits a gapped phase with effective color code behavior

High-energy excitations are three families of strongly interacting anyonic fermions

The system has a Z_2xZ_2 gauge symmetry and string-net integrals of motion

Abstract

We introduce a two-body quantum Hamiltonian model of spin-1/2 on a 2D spatial lattice with exact topological degeneracy in all coupling regimes. There exists a gapped phase in which the low-energy sector reproduces an effective color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. The model exhibits a Z_2xZ_2 gauge group symmetry and string-net integrals of motion, which are related to the existence of topological charges that are invisible to moving high-energy fermions.